Of course they would, the BBC has lunatics phoning in all the time with batshit conspiracy theories. You need only listen to Jeremy Vine on BBC for more than half an hour before someone insane calls in. That's when they're promptly challenged, questioned and revealed to be the superficial idiots they are under the slightest bit of pressure by an unbiased public media journalist. Putting the idiots in the spotlight has been a BBC tradition for as long as I can remember.

The BBC is nationally funded with tax payers money, it has a duty to be impartial without ceding the microphone to every idiot. Joe Rogan, on the Joe Rogan podcast, featuring Joe Rogan and paid for by his subscribers is under no such obligation to be impartial. People can (and did) pressure his broadcaster to make him stop - they could've pulled the plug but they elected to reprimand him and he said sorry.

Nutballs have every right to spew information and others have the right to challenge them and to put pressure on their privately owned platforms to stop them. My understanding of free speech is absolutely fine - it's decidedly Chomsky-esque and Twitter (and spotify) would therefore be wrong or misguided to dabble in it one way or another. Your idea of free speech applies to people who agrees with you and any of the opinions that concord with your world view. Everyone else can safely be considered a nut job and are best silenced for 'public safety' and 'saving lives'.